In triangle prs above, rt is the altitude to side ps and qs is the altitude to side pr. if rt = 7, pr = 8, and qs = 9, what is the length of ps?

In the given triangle PRS, QS and RT are the altitudes. An altitude of a triangle is a line segment through a vertex and perpendicular to form a right angle with a line containing the base.

Area of triangle with an altitude = \frac{1}{2}\times base \times height

Area of the triangle with base PR and altitude QS = \frac{1}{2}\times PR \times QS

= \frac{1}{2}\times 8 \times 9 = \frac{72}{2}.

Area of the triangle with base PS and altitude RT = \frac{1}{2}\times PS \times RT

= \frac{1}{2}\times PS \times 7 = \frac{7PS}{2}.

by equating both the areas, we get,

\frac{72}{2}=\frac{7PS}{2}

PS=\frac{72}{7}= 10.3

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